Fractional Anisotropy (FA)¶
Fractional Anisotropy (FA) is a scalar value that quantifies the degree of anisotropy (directional dependence) in a tensor field. In cardiotensor, FA is derived from the structure tensor eigenvalues and helps identify regions with organized myocardial fiber orientation.
Definition¶
Given the ordered eigenvalues of the structure tensor \(\lambda_1 \leq \lambda_2 \leq \lambda_3\), the FA is computed as:
\[
FA = \sqrt{\frac{3}{2}} \cdot \frac{\sqrt{(\lambda_1 - \bar{\lambda})^2 + (\lambda_2 - \bar{\lambda})^2 + (\lambda_3 - \bar{\lambda})^2}}{\sqrt{\lambda_1^2 + \lambda_2^2 + \lambda_3^2}}
\]
Where:
- \(\bar{\lambda} = (\lambda_1 + \lambda_2 + \lambda_3) / 3\): mean of the eigenvalues
Interpretation¶
- FA = 0: Isotropic region, where diffusion or structural orientation is equal in all directions (e.g. cavity or noise).
- FA = 1: Perfectly anisotropic region, structure is highly aligned in one direction (e.g. dense aligned fibers).
- 0 < FA < 1: Varying degrees of anisotropy.
This scalar map can be used to:
- Mask low-confidence areas for streamline seeding
- Identify anatomical regions of high or low alignment
- Visualize structural organization within the myocardium
Output¶
The FA volume is saved as a single 3D scalar field with the same shape as the input image:
It can be saved as TIFF or JP2 and visualized with standard volume rendering tools.
Thresholding in Tractography¶
FA values can be used to restrict streamline propagation:
- Minimum FA threshold: ensures streamlines are seeded and propagated only in structured regions
- Default values range from 0.1 to 0.2 depending on noise level and resolution